Can random matrix filters be used for trading in the foreign exchange market?-A comparison of foreign exchange and stock portfolio filtering

摘要: Markowitz portfolio theory [1], an intrinsic part of modern financial analysis, relies on the covariance matrix of returns and this can be difficult to estimate. For example, for a time series of length T, a portfolio of N assets requires (N2+ N)/2 covariances to be estimated from NT returns. This results in estimation noise, since the availability of historical information is limited. Moreover, it is commonly accepted that financial covariances are not fixed over time (eg [2–4]) and thus older historical data, even if available, can lead to cumulative noise effects.Random matrix theory (RMT), first developed by authors such as Dyson and Mehta [5–8], to explain the energy levels of complex nuclei [9], has recently been applied,(by several authors including Plerou et al.[9–13] and Laloux et al.[14, 15]), to noise filtering in financial time series, particularly in high dimensional systems such as stock markets. Both groups have analysed US …